On the stable equivalences between finite tensor categories
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY(2022)
Abstract
We aim to study Morita theory for tensor triangulated categories. For two finite tensor categories having no projective simple objects, we prove that their stable equivalence induced by an exact $\Bbbk$-linear monoidal functor can be lifted to a tensor equivalence under some certain conditions.
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Key words
Hopf algebra,stable categories,tensor categories,Frobenius-Perron dimensions
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